Search

We prove that the classic logarithmic barrier problem is equivalent to a particular logarithmic barrier positive relaxation problem with barrier and scaling parameters. Based on the equivalence, a line-search primal-dual interior-point relaxation method for nonlinear programs is presented. Our method does not require any primal or dual iterates to be interior-points, which has similarity to some warmstarting interior-point methods and is different from most of the globally convergent interior-point methods in the literature. A new logarithmic barrier penalty function dependent on both primal and dual variables is used to prompt the global convergence of the method, where the penalty parameter is adaptively updated. Without assuming any regularity condition, it is proved that our method will either terminate at an approximate KKT point of the original problem, an approximate infeasible stationary point, or an approximate singular stationary point of the original problem. Some preliminary numerical results are reported, including the results for a well-posed problem for which many line-search interior-point methods were demonstrated not to be globally convergent, a feasible problem for which the LICQ and the MFCQ fail to hold at the solution and an infeasible problem, and for some standard test problems of the CUTE collection. Correspondingly, for comparison we also report the numerical results obtained by the interior-point solver IPOPT. These results show that our algorithm is not only efficient for well-posed feasible problems, but is also applicable for some feasible problems without LICQ or MFCQ and some infeasible problems. [ABSTRACT FROM AUTHOR]

With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmic-barrier problems of nonlinear programs. As a result, a two-parameter primal-dual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point if the original problem is feasible, and it can be superlinearly or quadratically convergent to the infeasible stationary point when the problem is infeasible. Preliminary numerical results show that the method is efficient in solving some simple but hard problems, where the superlinear convergence to an infeasible stationary point is demonstrated when we solve two infeasible problems in the literature. [ABSTRACT FROM AUTHOR]

Purpose: An association between catechol-O-methyltransferase (COMT) 158G/A polymorphism and endometriosis/adenomyosis susceptibility has been reported in the previous studies, but the results were inconsistent. This study was conducted to explore this association in the Chinese population using meta-analysis.Materials and Methods: PubMed, Springer Link, Ovid, Chinese Wanfang Data Knowledge Service Platform, Chinese National Knowledge Infrastructure, and Chinese Biology Medicine were searched for all relevant studies published up to December 2015. The odds ratios (ORs) and 95% confidence intervals (CIs) were calculated to estimate the strength of the associations.Results: A total of 7 case-control studies including 782 cases and 700 controls were included in this meta-analysis. Overall, COMT 158G/A polymorphism was found to be significantly associated with endometriosis and adenomyosis risk in the Chinese population (A vs. G, OR = 1.21, 95% CI: 1.02-1.42; AA vs. GG, OR = 1.47, 95% CI: 1.01-2.14; AA vs. GG + GA, OR = 1.42, 95% CI: 0.99-2.03; AA + GA vs. GG, OR = 1.20, 95% CI: 0.97-1.49). In subgroup analyses stratified by ethnicity, source of controls and disease groups, the significant risk was found in Chinese not mentioned the ethnicity, in population-based studies and adenomyosis.Conclusions: COMT 158G/A polymorphism may contribute to the risk of endometriosis and adenomyosis in Chinese, particularly for adenomyosis. [ABSTRACT FROM AUTHOR]